Wiki source code of Real analysis II, fall 2015

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1 = Real analysis II, fall 2015 =
2
3
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5 {{panel}}
6 **Teacher:** [[Pertti Mattila>>doc:mathstatHenkilokunta.Mattila, Pertti]]
7
8 **Scope:** 10 cr
9
10 **Type:** Advanced studies
11
12 **Teaching: **
13 Weeks 36-42 and 44-50, Wednesday and Thursday 14-16 in room C122. First lecture Wednesday, September 2.
14
15 **The last lecture and exercise session will be on December 3.**
16
17 **The exams** **will be on December 10 and 21.
18 **
19
20 **Topics:**
21
22 Real analysis II is an advanced course on general measure and integration theory and analysis in Euclidean spaces. It is based on and continues the courses  "Mitta ja integraali" ja "Reaalianalyysi I".
23
24 **Contents:**
25
26 * Extension and uniqueness theorems for measures
27 * Product measures and  Fubini's theorem
28 * Hausdorff measures and dimension
29 * Weak topology of measures
30 * Mass distribution principle and Frostman's lemma
31 * Besicovitch and Vitali covering theorems
32 * Differentiation of measures and the Radon-Nikodym theorem
33 * Rademacher's theorem (differentiability of Lipschitz functions)
34 * Whitney's covering and extension theorem
35
36 === Course material:** Ilkka Holopainen: Moderni reaalianalyysi (in Finnish)
37 ** ===
38
39 * [[attach:MoRA.pdf]]
40
41 **Additional lecture notes:**
42
43 [[attach:ra2-lecture_notes.pdf]]
44
45 Books partially related to the course
46
47 * A.M. Bruckner, J.B. Bruckner and B. Thomson: Real Analysis (Prentice Hall)
48 * L. Evans & R. Gariepy: Measure theory and fine properties of functions (CRC Press)
49 * K. Falconer: Fractal geometry: Mathematical foundations and applications (Wiley & Sons)
50 * K. Falconer: The Geometry of Fractal Sets (Cambridge University Press)
51 * F. Jones: Lebesgue integration on Euclidean spaces (Jones and Bartlett)
52 * P. Mattila: Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability (Cambridge University Press)
53 * W. Rudin: Real and complex analysis (McGraw-Hill)
54
55 **Prerequisites:
56 **Basics on Lebesgue measure and integral
57 {{/panel}}
58
59
60
61 == News ==
62
63 *
64
65 == Exams ==
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67
68
69 == [[Registration>>url:https://oodi-www.it.helsinki.fi/hy/opintjakstied.jsp?html=1&Tunniste=57242||shape="rect"]] ==
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71
72 (% style="color: rgb(96,96,96);" %)Did you forget to register? (%%)[[What to do?>>url:https://wiki.helsinki.fi/display/mathstatOpiskelu/Kysymys4||style="text-decoration: underline;" shape="rect"]]
73
74 == Exercises ==
75
76 Exercise sessions will be on Thursdays 16-18 in B322.
77
78 [[attach:raII-1.pdf]]
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80 [[attach:raII-2.pdf]]
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82 [[attach:raII_3.pdf]]
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84 [[attach:raII_4.pdf]]
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86 [[attach:raII_5.pdf]]
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88 [[attach:raII_6.pdf]]
89
90 [[attach:raII_7.pdf]]
91
92 [[attach:raII_8.pdf]]
93
94 [[attach:raII_9.pdf]]
95
96 [[attach:raII_10.pdf]]
97
98 Suggestions for solutions by Jesse Jääsaari
99
100 [[attach:ra1.pdf]]
101
102 [[attach:ra2.pdf]]
103
104 [[attach:ra3.pdf]]
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106 [[attach:ra4.pdf]]
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108 [[attach:ra5.pdf]]
109
110 [[attach:ra6.pdf]]
111
112 [[attach:ra7.pdf]]
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114 [[attach:ra8.pdf]]
115
116 [[attach:ra9.pdf]]
117
118 [[attach:ra10.pdf]]
119
120 === Assignment ===
121
122 === Exercise classes ===
123
124 |=(((
125 Group
126 )))|=(((
127 Day
128 )))|=(((
129 Time
130 )))|=(((
131 Room
132 )))|=(% colspan="1" %)(((
133 Instructor
134 )))
135 |(((
136 1.
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138 Thursday
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140 16-18
141 )))|(((
142 B322
143 )))|(% colspan="1" %)(((
144 Pertti Mattila
145 )))
146
147 == Course feedback ==
148
149 Course feedback can be given at any point during the course. Click [[here>>url:https://elomake.helsinki.fi/lomakkeet/11954/lomake.html||style="line-height: 1.4285;" shape="rect"]].